diff -r c6acc34f98dc -r 1a7fe3bef514 lemon/lp_base.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/lp_base.h	Thu Nov 05 15:50:01 2009 +0100
@@ -0,0 +1,2102 @@
+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_LP_BASE_H
+#define LEMON_LP_BASE_H
+
+#include<iostream>
+#include<vector>
+#include<map>
+#include<limits>
+#include<lemon/math.h>
+
+#include<lemon/error.h>
+#include<lemon/assert.h>
+
+#include<lemon/core.h>
+#include<lemon/bits/solver_bits.h>
+
+///\file
+///\brief The interface of the LP solver interface.
+///\ingroup lp_group
+namespace lemon {
+
+  ///Common base class for LP and MIP solvers
+
+  ///Usually this class is not used directly, please use one of the concrete
+  ///implementations of the solver interface.
+  ///\ingroup lp_group
+  class LpBase {
+
+  protected:
+
+    _solver_bits::VarIndex rows;
+    _solver_bits::VarIndex cols;
+
+  public:
+
+    ///Possible outcomes of an LP solving procedure
+    enum SolveExitStatus {
+      /// = 0. It means that the problem has been successfully solved: either
+      ///an optimal solution has been found or infeasibility/unboundedness
+      ///has been proved.
+      SOLVED = 0,
+      /// = 1. Any other case (including the case when some user specified
+      ///limit has been exceeded).
+      UNSOLVED = 1
+    };
+
+    ///Direction of the optimization
+    enum Sense {
+      /// Minimization
+      MIN,
+      /// Maximization
+      MAX
+    };
+
+    ///Enum for \c messageLevel() parameter
+    enum MessageLevel {
+      /// No output (default value).
+      MESSAGE_NOTHING,
+      /// Error messages only.
+      MESSAGE_ERROR,
+      /// Warnings.
+      MESSAGE_WARNING,
+      /// Normal output.
+      MESSAGE_NORMAL,
+      /// Verbose output.
+      MESSAGE_VERBOSE
+    };
+    
+
+    ///The floating point type used by the solver
+    typedef double Value;
+    ///The infinity constant
+    static const Value INF;
+    ///The not a number constant
+    static const Value NaN;
+
+    friend class Col;
+    friend class ColIt;
+    friend class Row;
+    friend class RowIt;
+
+    ///Refer to a column of the LP.
+
+    ///This type is used to refer to a column of the LP.
+    ///
+    ///Its value remains valid and correct even after the addition or erase of
+    ///other columns.
+    ///
+    ///\note This class is similar to other Item types in LEMON, like
+    ///Node and Arc types in digraph.
+    class Col {
+      friend class LpBase;
+    protected:
+      int _id;
+      explicit Col(int id) : _id(id) {}
+    public:
+      typedef Value ExprValue;
+      typedef True LpCol;
+      /// Default constructor
+      
+      /// \warning The default constructor sets the Col to an
+      /// undefined value.
+      Col() {}
+      /// Invalid constructor \& conversion.
+      
+      /// This constructor initializes the Col to be invalid.
+      /// \sa Invalid for more details.      
+      Col(const Invalid&) : _id(-1) {}
+      /// Equality operator
+
+      /// Two \ref Col "Col"s are equal if and only if they point to
+      /// the same LP column or both are invalid.
+      bool operator==(Col c) const  {return _id == c._id;}
+      /// Inequality operator
+
+      /// \sa operator==(Col c)
+      ///
+      bool operator!=(Col c) const  {return _id != c._id;}
+      /// Artificial ordering operator.
+
+      /// To allow the use of this object in std::map or similar
+      /// associative container we require this.
+      ///
+      /// \note This operator only have to define some strict ordering of
+      /// the items; this order has nothing to do with the iteration
+      /// ordering of the items.
+      bool operator<(Col c) const  {return _id < c._id;}
+    };
+
+    ///Iterator for iterate over the columns of an LP problem
+
+    /// Its usage is quite simple, for example you can count the number
+    /// of columns in an LP \c lp:
+    ///\code
+    /// int count=0;
+    /// for (LpBase::ColIt c(lp); c!=INVALID; ++c) ++count;
+    ///\endcode
+    class ColIt : public Col {
+      const LpBase *_solver;
+    public:
+      /// Default constructor
+      
+      /// \warning The default constructor sets the iterator
+      /// to an undefined value.
+      ColIt() {}
+      /// Sets the iterator to the first Col
+      
+      /// Sets the iterator to the first Col.
+      ///
+      ColIt(const LpBase &solver) : _solver(&solver)
+      {
+        _solver->cols.firstItem(_id);
+      }
+      /// Invalid constructor \& conversion
+      
+      /// Initialize the iterator to be invalid.
+      /// \sa Invalid for more details.
+      ColIt(const Invalid&) : Col(INVALID) {}
+      /// Next column
+      
+      /// Assign the iterator to the next column.
+      ///
+      ColIt &operator++()
+      {
+        _solver->cols.nextItem(_id);
+        return *this;
+      }
+    };
+
+    /// \brief Returns the ID of the column.
+    static int id(const Col& col) { return col._id; }
+    /// \brief Returns the column with the given ID.
+    ///
+    /// \pre The argument should be a valid column ID in the LP problem.
+    static Col colFromId(int id) { return Col(id); }
+
+    ///Refer to a row of the LP.
+
+    ///This type is used to refer to a row of the LP.
+    ///
+    ///Its value remains valid and correct even after the addition or erase of
+    ///other rows.
+    ///
+    ///\note This class is similar to other Item types in LEMON, like
+    ///Node and Arc types in digraph.
+    class Row {
+      friend class LpBase;
+    protected:
+      int _id;
+      explicit Row(int id) : _id(id) {}
+    public:
+      typedef Value ExprValue;
+      typedef True LpRow;
+      /// Default constructor
+      
+      /// \warning The default constructor sets the Row to an
+      /// undefined value.
+      Row() {}
+      /// Invalid constructor \& conversion.
+      
+      /// This constructor initializes the Row to be invalid.
+      /// \sa Invalid for more details.      
+      Row(const Invalid&) : _id(-1) {}
+      /// Equality operator
+
+      /// Two \ref Row "Row"s are equal if and only if they point to
+      /// the same LP row or both are invalid.
+      bool operator==(Row r) const  {return _id == r._id;}
+      /// Inequality operator
+      
+      /// \sa operator==(Row r)
+      ///
+      bool operator!=(Row r) const  {return _id != r._id;}
+      /// Artificial ordering operator.
+
+      /// To allow the use of this object in std::map or similar
+      /// associative container we require this.
+      ///
+      /// \note This operator only have to define some strict ordering of
+      /// the items; this order has nothing to do with the iteration
+      /// ordering of the items.
+      bool operator<(Row r) const  {return _id < r._id;}
+    };
+
+    ///Iterator for iterate over the rows of an LP problem
+
+    /// Its usage is quite simple, for example you can count the number
+    /// of rows in an LP \c lp:
+    ///\code
+    /// int count=0;
+    /// for (LpBase::RowIt c(lp); c!=INVALID; ++c) ++count;
+    ///\endcode
+    class RowIt : public Row {
+      const LpBase *_solver;
+    public:
+      /// Default constructor
+      
+      /// \warning The default constructor sets the iterator
+      /// to an undefined value.
+      RowIt() {}
+      /// Sets the iterator to the first Row
+      
+      /// Sets the iterator to the first Row.
+      ///
+      RowIt(const LpBase &solver) : _solver(&solver)
+      {
+        _solver->rows.firstItem(_id);
+      }
+      /// Invalid constructor \& conversion
+      
+      /// Initialize the iterator to be invalid.
+      /// \sa Invalid for more details.
+      RowIt(const Invalid&) : Row(INVALID) {}
+      /// Next row
+      
+      /// Assign the iterator to the next row.
+      ///
+      RowIt &operator++()
+      {
+        _solver->rows.nextItem(_id);
+        return *this;
+      }
+    };
+
+    /// \brief Returns the ID of the row.
+    static int id(const Row& row) { return row._id; }
+    /// \brief Returns the row with the given ID.
+    ///
+    /// \pre The argument should be a valid row ID in the LP problem.
+    static Row rowFromId(int id) { return Row(id); }
+
+  public:
+
+    ///Linear expression of variables and a constant component
+
+    ///This data structure stores a linear expression of the variables
+    ///(\ref Col "Col"s) and also has a constant component.
+    ///
+    ///There are several ways to access and modify the contents of this
+    ///container.
+    ///\code
+    ///e[v]=5;
+    ///e[v]+=12;
+    ///e.erase(v);
+    ///\endcode
+    ///or you can also iterate through its elements.
+    ///\code
+    ///double s=0;
+    ///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
+    ///  s+=*i * primal(i);
+    ///\endcode
+    ///(This code computes the primal value of the expression).
+    ///- Numbers (<tt>double</tt>'s)
+    ///and variables (\ref Col "Col"s) directly convert to an
+    ///\ref Expr and the usual linear operations are defined, so
+    ///\code
+    ///v+w
+    ///2*v-3.12*(v-w/2)+2
+    ///v*2.1+(3*v+(v*12+w+6)*3)/2
+    ///\endcode
+    ///are valid expressions.
+    ///The usual assignment operations are also defined.
+    ///\code
+    ///e=v+w;
+    ///e+=2*v-3.12*(v-w/2)+2;
+    ///e*=3.4;
+    ///e/=5;
+    ///\endcode
+    ///- The constant member can be set and read by dereference
+    ///  operator (unary *)
+    ///
+    ///\code
+    ///*e=12;
+    ///double c=*e;
+    ///\endcode
+    ///
+    ///\sa Constr
+    class Expr {
+      friend class LpBase;
+    public:
+      /// The key type of the expression
+      typedef LpBase::Col Key;
+      /// The value type of the expression
+      typedef LpBase::Value Value;
+
+    protected:
+      Value const_comp;
+      std::map<int, Value> comps;
+
+    public:
+      typedef True SolverExpr;
+      /// Default constructor
+      
+      /// Construct an empty expression, the coefficients and
+      /// the constant component are initialized to zero.
+      Expr() : const_comp(0) {}
+      /// Construct an expression from a column
+
+      /// Construct an expression, which has a term with \c c variable
+      /// and 1.0 coefficient.
+      Expr(const Col &c) : const_comp(0) {
+        typedef std::map<int, Value>::value_type pair_type;
+        comps.insert(pair_type(id(c), 1));
+      }
+      /// Construct an expression from a constant
+
+      /// Construct an expression, which's constant component is \c v.
+      ///
+      Expr(const Value &v) : const_comp(v) {}
+      /// Returns the coefficient of the column
+      Value operator[](const Col& c) const {
+        std::map<int, Value>::const_iterator it=comps.find(id(c));
+        if (it != comps.end()) {
+          return it->second;
+        } else {
+          return 0;
+        }
+      }
+      /// Returns the coefficient of the column
+      Value& operator[](const Col& c) {
+        return comps[id(c)];
+      }
+      /// Sets the coefficient of the column
+      void set(const Col &c, const Value &v) {
+        if (v != 0.0) {
+          typedef std::map<int, Value>::value_type pair_type;
+          comps.insert(pair_type(id(c), v));
+        } else {
+          comps.erase(id(c));
+        }
+      }
+      /// Returns the constant component of the expression
+      Value& operator*() { return const_comp; }
+      /// Returns the constant component of the expression
+      const Value& operator*() const { return const_comp; }
+      /// \brief Removes the coefficients which's absolute value does
+      /// not exceed \c epsilon. It also sets to zero the constant
+      /// component, if it does not exceed epsilon in absolute value.
+      void simplify(Value epsilon = 0.0) {
+        std::map<int, Value>::iterator it=comps.begin();
+        while (it != comps.end()) {
+          std::map<int, Value>::iterator jt=it;
+          ++jt;
+          if (std::fabs((*it).second) <= epsilon) comps.erase(it);
+          it=jt;
+        }
+        if (std::fabs(const_comp) <= epsilon) const_comp = 0;
+      }
+
+      void simplify(Value epsilon = 0.0) const {
+        const_cast<Expr*>(this)->simplify(epsilon);
+      }
+
+      ///Sets all coefficients and the constant component to 0.
+      void clear() {
+        comps.clear();
+        const_comp=0;
+      }
+
+      ///Compound assignment
+      Expr &operator+=(const Expr &e) {
+        for (std::map<int, Value>::const_iterator it=e.comps.begin();
+             it!=e.comps.end(); ++it)
+          comps[it->first]+=it->second;
+        const_comp+=e.const_comp;
+        return *this;
+      }
+      ///Compound assignment
+      Expr &operator-=(const Expr &e) {
+        for (std::map<int, Value>::const_iterator it=e.comps.begin();
+             it!=e.comps.end(); ++it)
+          comps[it->first]-=it->second;
+        const_comp-=e.const_comp;
+        return *this;
+      }
+      ///Multiply with a constant
+      Expr &operator*=(const Value &v) {
+        for (std::map<int, Value>::iterator it=comps.begin();
+             it!=comps.end(); ++it)
+          it->second*=v;
+        const_comp*=v;
+        return *this;
+      }
+      ///Division with a constant
+      Expr &operator/=(const Value &c) {
+        for (std::map<int, Value>::iterator it=comps.begin();
+             it!=comps.end(); ++it)
+          it->second/=c;
+        const_comp/=c;
+        return *this;
+      }
+
+      ///Iterator over the expression
+      
+      ///The iterator iterates over the terms of the expression. 
+      /// 
+      ///\code
+      ///double s=0;
+      ///for(LpBase::Expr::CoeffIt i(e);i!=INVALID;++i)
+      ///  s+= *i * primal(i);
+      ///\endcode
+      class CoeffIt {
+      private:
+
+        std::map<int, Value>::iterator _it, _end;
+
+      public:
+
+        /// Sets the iterator to the first term
+        
+        /// Sets the iterator to the first term of the expression.
+        ///
+        CoeffIt(Expr& e)
+          : _it(e.comps.begin()), _end(e.comps.end()){}
+
+        /// Convert the iterator to the column of the term
+        operator Col() const {
+          return colFromId(_it->first);
+        }
+
+        /// Returns the coefficient of the term
+        Value& operator*() { return _it->second; }
+
+        /// Returns the coefficient of the term
+        const Value& operator*() const { return _it->second; }
+        /// Next term
+        
+        /// Assign the iterator to the next term.
+        ///
+        CoeffIt& operator++() { ++_it; return *this; }
+
+        /// Equality operator
+        bool operator==(Invalid) const { return _it == _end; }
+        /// Inequality operator
+        bool operator!=(Invalid) const { return _it != _end; }
+      };
+
+      /// Const iterator over the expression
+      
+      ///The iterator iterates over the terms of the expression. 
+      /// 
+      ///\code
+      ///double s=0;
+      ///for(LpBase::Expr::ConstCoeffIt i(e);i!=INVALID;++i)
+      ///  s+=*i * primal(i);
+      ///\endcode
+      class ConstCoeffIt {
+      private:
+
+        std::map<int, Value>::const_iterator _it, _end;
+
+      public:
+
+        /// Sets the iterator to the first term
+        
+        /// Sets the iterator to the first term of the expression.
+        ///
+        ConstCoeffIt(const Expr& e)
+          : _it(e.comps.begin()), _end(e.comps.end()){}
+
+        /// Convert the iterator to the column of the term
+        operator Col() const {
+          return colFromId(_it->first);
+        }
+
+        /// Returns the coefficient of the term
+        const Value& operator*() const { return _it->second; }
+
+        /// Next term
+        
+        /// Assign the iterator to the next term.
+        ///
+        ConstCoeffIt& operator++() { ++_it; return *this; }
+
+        /// Equality operator
+        bool operator==(Invalid) const { return _it == _end; }
+        /// Inequality operator
+        bool operator!=(Invalid) const { return _it != _end; }
+      };
+
+    };
+
+    ///Linear constraint
+
+    ///This data stucture represents a linear constraint in the LP.
+    ///Basically it is a linear expression with a lower or an upper bound
+    ///(or both). These parts of the constraint can be obtained by the member
+    ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
+    ///respectively.
+    ///There are two ways to construct a constraint.
+    ///- You can set the linear expression and the bounds directly
+    ///  by the functions above.
+    ///- The operators <tt>\<=</tt>, <tt>==</tt> and  <tt>\>=</tt>
+    ///  are defined between expressions, or even between constraints whenever
+    ///  it makes sense. Therefore if \c e and \c f are linear expressions and
+    ///  \c s and \c t are numbers, then the followings are valid expressions
+    ///  and thus they can be used directly e.g. in \ref addRow() whenever
+    ///  it makes sense.
+    ///\code
+    ///  e<=s
+    ///  e<=f
+    ///  e==f
+    ///  s<=e<=t
+    ///  e>=t
+    ///\endcode
+    ///\warning The validity of a constraint is checked only at run
+    ///time, so e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will
+    ///compile, but will fail an assertion.
+    class Constr
+    {
+    public:
+      typedef LpBase::Expr Expr;
+      typedef Expr::Key Key;
+      typedef Expr::Value Value;
+
+    protected:
+      Expr _expr;
+      Value _lb,_ub;
+    public:
+      ///\e
+      Constr() : _expr(), _lb(NaN), _ub(NaN) {}
+      ///\e
+      Constr(Value lb, const Expr &e, Value ub) :
+        _expr(e), _lb(lb), _ub(ub) {}
+      Constr(const Expr &e) :
+        _expr(e), _lb(NaN), _ub(NaN) {}
+      ///\e
+      void clear()
+      {
+        _expr.clear();
+        _lb=_ub=NaN;
+      }
+
+      ///Reference to the linear expression
+      Expr &expr() { return _expr; }
+      ///Cont reference to the linear expression
+      const Expr &expr() const { return _expr; }
+      ///Reference to the lower bound.
+
+      ///\return
+      ///- \ref INF "INF": the constraint is lower unbounded.
+      ///- \ref NaN "NaN": lower bound has not been set.
+      ///- finite number: the lower bound
+      Value &lowerBound() { return _lb; }
+      ///The const version of \ref lowerBound()
+      const Value &lowerBound() const { return _lb; }
+      ///Reference to the upper bound.
+
+      ///\return
+      ///- \ref INF "INF": the constraint is upper unbounded.
+      ///- \ref NaN "NaN": upper bound has not been set.
+      ///- finite number: the upper bound
+      Value &upperBound() { return _ub; }
+      ///The const version of \ref upperBound()
+      const Value &upperBound() const { return _ub; }
+      ///Is the constraint lower bounded?
+      bool lowerBounded() const {
+        return _lb != -INF && !isNaN(_lb);
+      }
+      ///Is the constraint upper bounded?
+      bool upperBounded() const {
+        return _ub != INF && !isNaN(_ub);
+      }
+
+    };
+
+    ///Linear expression of rows
+
+    ///This data structure represents a column of the matrix,
+    ///thas is it strores a linear expression of the dual variables
+    ///(\ref Row "Row"s).
+    ///
+    ///There are several ways to access and modify the contents of this
+    ///container.
+    ///\code
+    ///e[v]=5;
+    ///e[v]+=12;
+    ///e.erase(v);
+    ///\endcode
+    ///or you can also iterate through its elements.
+    ///\code
+    ///double s=0;
+    ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
+    ///  s+=*i;
+    ///\endcode
+    ///(This code computes the sum of all coefficients).
+    ///- Numbers (<tt>double</tt>'s)
+    ///and variables (\ref Row "Row"s) directly convert to an
+    ///\ref DualExpr and the usual linear operations are defined, so
+    ///\code
+    ///v+w
+    ///2*v-3.12*(v-w/2)
+    ///v*2.1+(3*v+(v*12+w)*3)/2
+    ///\endcode
+    ///are valid \ref DualExpr dual expressions.
+    ///The usual assignment operations are also defined.
+    ///\code
+    ///e=v+w;
+    ///e+=2*v-3.12*(v-w/2);
+    ///e*=3.4;
+    ///e/=5;
+    ///\endcode
+    ///
+    ///\sa Expr
+    class DualExpr {
+      friend class LpBase;
+    public:
+      /// The key type of the expression
+      typedef LpBase::Row Key;
+      /// The value type of the expression
+      typedef LpBase::Value Value;
+
+    protected:
+      std::map<int, Value> comps;
+
+    public:
+      typedef True SolverExpr;
+      /// Default constructor
+      
+      /// Construct an empty expression, the coefficients are
+      /// initialized to zero.
+      DualExpr() {}
+      /// Construct an expression from a row
+
+      /// Construct an expression, which has a term with \c r dual
+      /// variable and 1.0 coefficient.
+      DualExpr(const Row &r) {
+        typedef std::map<int, Value>::value_type pair_type;
+        comps.insert(pair_type(id(r), 1));
+      }
+      /// Returns the coefficient of the row
+      Value operator[](const Row& r) const {
+        std::map<int, Value>::const_iterator it = comps.find(id(r));
+        if (it != comps.end()) {
+          return it->second;
+        } else {
+          return 0;
+        }
+      }
+      /// Returns the coefficient of the row
+      Value& operator[](const Row& r) {
+        return comps[id(r)];
+      }
+      /// Sets the coefficient of the row
+      void set(const Row &r, const Value &v) {
+        if (v != 0.0) {
+          typedef std::map<int, Value>::value_type pair_type;
+          comps.insert(pair_type(id(r), v));
+        } else {
+          comps.erase(id(r));
+        }
+      }
+      /// \brief Removes the coefficients which's absolute value does
+      /// not exceed \c epsilon. 
+      void simplify(Value epsilon = 0.0) {
+        std::map<int, Value>::iterator it=comps.begin();
+        while (it != comps.end()) {
+          std::map<int, Value>::iterator jt=it;
+          ++jt;
+          if (std::fabs((*it).second) <= epsilon) comps.erase(it);
+          it=jt;
+        }
+      }
+
+      void simplify(Value epsilon = 0.0) const {
+        const_cast<DualExpr*>(this)->simplify(epsilon);
+      }
+
+      ///Sets all coefficients to 0.
+      void clear() {
+        comps.clear();
+      }
+      ///Compound assignment
+      DualExpr &operator+=(const DualExpr &e) {
+        for (std::map<int, Value>::const_iterator it=e.comps.begin();
+             it!=e.comps.end(); ++it)
+          comps[it->first]+=it->second;
+        return *this;
+      }
+      ///Compound assignment
+      DualExpr &operator-=(const DualExpr &e) {
+        for (std::map<int, Value>::const_iterator it=e.comps.begin();
+             it!=e.comps.end(); ++it)
+          comps[it->first]-=it->second;
+        return *this;
+      }
+      ///Multiply with a constant
+      DualExpr &operator*=(const Value &v) {
+        for (std::map<int, Value>::iterator it=comps.begin();
+             it!=comps.end(); ++it)
+          it->second*=v;
+        return *this;
+      }
+      ///Division with a constant
+      DualExpr &operator/=(const Value &v) {
+        for (std::map<int, Value>::iterator it=comps.begin();
+             it!=comps.end(); ++it)
+          it->second/=v;
+        return *this;
+      }
+
+      ///Iterator over the expression
+      
+      ///The iterator iterates over the terms of the expression. 
+      /// 
+      ///\code
+      ///double s=0;
+      ///for(LpBase::DualExpr::CoeffIt i(e);i!=INVALID;++i)
+      ///  s+= *i * dual(i);
+      ///\endcode
+      class CoeffIt {
+      private:
+
+        std::map<int, Value>::iterator _it, _end;
+
+      public:
+
+        /// Sets the iterator to the first term
+        
+        /// Sets the iterator to the first term of the expression.
+        ///
+        CoeffIt(DualExpr& e)
+          : _it(e.comps.begin()), _end(e.comps.end()){}
+
+        /// Convert the iterator to the row of the term
+        operator Row() const {
+          return rowFromId(_it->first);
+        }
+
+        /// Returns the coefficient of the term
+        Value& operator*() { return _it->second; }
+
+        /// Returns the coefficient of the term
+        const Value& operator*() const { return _it->second; }
+
+        /// Next term
+        
+        /// Assign the iterator to the next term.
+        ///
+        CoeffIt& operator++() { ++_it; return *this; }
+
+        /// Equality operator
+        bool operator==(Invalid) const { return _it == _end; }
+        /// Inequality operator
+        bool operator!=(Invalid) const { return _it != _end; }
+      };
+
+      ///Iterator over the expression
+      
+      ///The iterator iterates over the terms of the expression. 
+      /// 
+      ///\code
+      ///double s=0;
+      ///for(LpBase::DualExpr::ConstCoeffIt i(e);i!=INVALID;++i)
+      ///  s+= *i * dual(i);
+      ///\endcode
+      class ConstCoeffIt {
+      private:
+
+        std::map<int, Value>::const_iterator _it, _end;
+
+      public:
+
+        /// Sets the iterator to the first term
+        
+        /// Sets the iterator to the first term of the expression.
+        ///
+        ConstCoeffIt(const DualExpr& e)
+          : _it(e.comps.begin()), _end(e.comps.end()){}
+
+        /// Convert the iterator to the row of the term
+        operator Row() const {
+          return rowFromId(_it->first);
+        }
+
+        /// Returns the coefficient of the term
+        const Value& operator*() const { return _it->second; }
+
+        /// Next term
+        
+        /// Assign the iterator to the next term.
+        ///
+        ConstCoeffIt& operator++() { ++_it; return *this; }
+
+        /// Equality operator
+        bool operator==(Invalid) const { return _it == _end; }
+        /// Inequality operator
+        bool operator!=(Invalid) const { return _it != _end; }
+      };
+    };
+
+
+  protected:
+
+    class InsertIterator {
+    private:
+
+      std::map<int, Value>& _host;
+      const _solver_bits::VarIndex& _index;
+
+    public:
+
+      typedef std::output_iterator_tag iterator_category;
+      typedef void difference_type;
+      typedef void value_type;
+      typedef void reference;
+      typedef void pointer;
+
+      InsertIterator(std::map<int, Value>& host,
+                   const _solver_bits::VarIndex& index)
+        : _host(host), _index(index) {}
+
+      InsertIterator& operator=(const std::pair<int, Value>& value) {
+        typedef std::map<int, Value>::value_type pair_type;
+        _host.insert(pair_type(_index[value.first], value.second));
+        return *this;
+      }
+
+      InsertIterator& operator*() { return *this; }
+      InsertIterator& operator++() { return *this; }
+      InsertIterator operator++(int) { return *this; }
+
+    };
+
+    class ExprIterator {
+    private:
+      std::map<int, Value>::const_iterator _host_it;
+      const _solver_bits::VarIndex& _index;
+    public:
+
+      typedef std::bidirectional_iterator_tag iterator_category;
+      typedef std::ptrdiff_t difference_type;
+      typedef const std::pair<int, Value> value_type;
+      typedef value_type reference;
+
+      class pointer {
+      public:
+        pointer(value_type& _value) : value(_value) {}
+        value_type* operator->() { return &value; }
+      private:
+        value_type value;
+      };
+
+      ExprIterator(const std::map<int, Value>::const_iterator& host_it,
+                   const _solver_bits::VarIndex& index)
+        : _host_it(host_it), _index(index) {}
+
+      reference operator*() {
+        return std::make_pair(_index(_host_it->first), _host_it->second);
+      }
+
+      pointer operator->() {
+        return pointer(operator*());
+      }
+
+      ExprIterator& operator++() { ++_host_it; return *this; }
+      ExprIterator operator++(int) {
+        ExprIterator tmp(*this); ++_host_it; return tmp;
+      }
+
+      ExprIterator& operator--() { --_host_it; return *this; }
+      ExprIterator operator--(int) {
+        ExprIterator tmp(*this); --_host_it; return tmp;
+      }
+
+      bool operator==(const ExprIterator& it) const {
+        return _host_it == it._host_it;
+      }
+
+      bool operator!=(const ExprIterator& it) const {
+        return _host_it != it._host_it;
+      }
+
+    };
+
+  protected:
+
+    //Abstract virtual functions
+
+    virtual int _addColId(int col) { return cols.addIndex(col); }
+    virtual int _addRowId(int row) { return rows.addIndex(row); }
+
+    virtual void _eraseColId(int col) { cols.eraseIndex(col); }
+    virtual void _eraseRowId(int row) { rows.eraseIndex(row); }
+
+    virtual int _addCol() = 0;
+    virtual int _addRow() = 0;
+
+    virtual int _addRow(Value l, ExprIterator b, ExprIterator e, Value u) {
+      int row = _addRow();
+      _setRowCoeffs(row, b, e);
+      _setRowLowerBound(row, l);
+      _setRowUpperBound(row, u);
+      return row;
+    }
+
+    virtual void _eraseCol(int col) = 0;
+    virtual void _eraseRow(int row) = 0;
+
+    virtual void _getColName(int col, std::string& name) const = 0;
+    virtual void _setColName(int col, const std::string& name) = 0;
+    virtual int _colByName(const std::string& name) const = 0;
+
+    virtual void _getRowName(int row, std::string& name) const = 0;
+    virtual void _setRowName(int row, const std::string& name) = 0;
+    virtual int _rowByName(const std::string& name) const = 0;
+
+    virtual void _setRowCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
+    virtual void _getRowCoeffs(int i, InsertIterator b) const = 0;
+
+    virtual void _setColCoeffs(int i, ExprIterator b, ExprIterator e) = 0;
+    virtual void _getColCoeffs(int i, InsertIterator b) const = 0;
+
+    virtual void _setCoeff(int row, int col, Value value) = 0;
+    virtual Value _getCoeff(int row, int col) const = 0;
+
+    virtual void _setColLowerBound(int i, Value value) = 0;
+    virtual Value _getColLowerBound(int i) const = 0;
+
+    virtual void _setColUpperBound(int i, Value value) = 0;
+    virtual Value _getColUpperBound(int i) const = 0;
+
+    virtual void _setRowLowerBound(int i, Value value) = 0;
+    virtual Value _getRowLowerBound(int i) const = 0;
+
+    virtual void _setRowUpperBound(int i, Value value) = 0;
+    virtual Value _getRowUpperBound(int i) const = 0;
+
+    virtual void _setObjCoeffs(ExprIterator b, ExprIterator e) = 0;
+    virtual void _getObjCoeffs(InsertIterator b) const = 0;
+
+    virtual void _setObjCoeff(int i, Value obj_coef) = 0;
+    virtual Value _getObjCoeff(int i) const = 0;
+
+    virtual void _setSense(Sense) = 0;
+    virtual Sense _getSense() const = 0;
+
+    virtual void _clear() = 0;
+
+    virtual const char* _solverName() const = 0;
+
+    virtual void _messageLevel(MessageLevel level) = 0;
+
+    //Own protected stuff
+
+    //Constant component of the objective function
+    Value obj_const_comp;
+
+    LpBase() : rows(), cols(), obj_const_comp(0) {}
+
+  public:
+
+    /// Virtual destructor
+    virtual ~LpBase() {}
+
+    ///Gives back the name of the solver.
+    const char* solverName() const {return _solverName();}
+
+    ///\name Build Up and Modify the LP
+
+    ///@{
+
+    ///Add a new empty column (i.e a new variable) to the LP
+    Col addCol() { Col c; c._id = _addColId(_addCol()); return c;}
+
+    ///\brief Adds several new columns (i.e variables) at once
+    ///
+    ///This magic function takes a container as its argument and fills
+    ///its elements with new columns (i.e. variables)
+    ///\param t can be
+    ///- a standard STL compatible iterable container with
+    ///\ref Col as its \c values_type like
+    ///\code
+    ///std::vector<LpBase::Col>
+    ///std::list<LpBase::Col>
+    ///\endcode
+    ///- a standard STL compatible iterable container with
+    ///\ref Col as its \c mapped_type like
+    ///\code
+    ///std::map<AnyType,LpBase::Col>
+    ///\endcode
+    ///- an iterable lemon \ref concepts::WriteMap "write map" like
+    ///\code
+    ///ListGraph::NodeMap<LpBase::Col>
+    ///ListGraph::ArcMap<LpBase::Col>
+    ///\endcode
+    ///\return The number of the created column.
+#ifdef DOXYGEN
+    template<class T>
+    int addColSet(T &t) { return 0;}
+#else
+    template<class T>
+    typename enable_if<typename T::value_type::LpCol,int>::type
+    addColSet(T &t,dummy<0> = 0) {
+      int s=0;
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
+      return s;
+    }
+    template<class T>
+    typename enable_if<typename T::value_type::second_type::LpCol,
+                       int>::type
+    addColSet(T &t,dummy<1> = 1) {
+      int s=0;
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        i->second=addCol();
+        s++;
+      }
+      return s;
+    }
+    template<class T>
+    typename enable_if<typename T::MapIt::Value::LpCol,
+                       int>::type
+    addColSet(T &t,dummy<2> = 2) {
+      int s=0;
+      for(typename T::MapIt i(t); i!=INVALID; ++i)
+        {
+          i.set(addCol());
+          s++;
+        }
+      return s;
+    }
+#endif
+
+    ///Set a column (i.e a dual constraint) of the LP
+
+    ///\param c is the column to be modified
+    ///\param e is a dual linear expression (see \ref DualExpr)
+    ///a better one.
+    void col(Col c, const DualExpr &e) {
+      e.simplify();
+      _setColCoeffs(cols(id(c)), ExprIterator(e.comps.begin(), rows),
+                    ExprIterator(e.comps.end(), rows));
+    }
+
+    ///Get a column (i.e a dual constraint) of the LP
+
+    ///\param c is the column to get
+    ///\return the dual expression associated to the column
+    DualExpr col(Col c) const {
+      DualExpr e;
+      _getColCoeffs(cols(id(c)), InsertIterator(e.comps, rows));
+      return e;
+    }
+
+    ///Add a new column to the LP
+
+    ///\param e is a dual linear expression (see \ref DualExpr)
+    ///\param o is the corresponding component of the objective
+    ///function. It is 0 by default.
+    ///\return The created column.
+    Col addCol(const DualExpr &e, Value o = 0) {
+      Col c=addCol();
+      col(c,e);
+      objCoeff(c,o);
+      return c;
+    }
+
+    ///Add a new empty row (i.e a new constraint) to the LP
+
+    ///This function adds a new empty row (i.e a new constraint) to the LP.
+    ///\return The created row
+    Row addRow() { Row r; r._id = _addRowId(_addRow()); return r;}
+
+    ///\brief Add several new rows (i.e constraints) at once
+    ///
+    ///This magic function takes a container as its argument and fills
+    ///its elements with new row (i.e. variables)
+    ///\param t can be
+    ///- a standard STL compatible iterable container with
+    ///\ref Row as its \c values_type like
+    ///\code
+    ///std::vector<LpBase::Row>
+    ///std::list<LpBase::Row>
+    ///\endcode
+    ///- a standard STL compatible iterable container with
+    ///\ref Row as its \c mapped_type like
+    ///\code
+    ///std::map<AnyType,LpBase::Row>
+    ///\endcode
+    ///- an iterable lemon \ref concepts::WriteMap "write map" like
+    ///\code
+    ///ListGraph::NodeMap<LpBase::Row>
+    ///ListGraph::ArcMap<LpBase::Row>
+    ///\endcode
+    ///\return The number of rows created.
+#ifdef DOXYGEN
+    template<class T>
+    int addRowSet(T &t) { return 0;}
+#else
+    template<class T>
+    typename enable_if<typename T::value_type::LpRow,int>::type
+    addRowSet(T &t, dummy<0> = 0) {
+      int s=0;
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
+      return s;
+    }
+    template<class T>
+    typename enable_if<typename T::value_type::second_type::LpRow, int>::type
+    addRowSet(T &t, dummy<1> = 1) {
+      int s=0;
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        i->second=addRow();
+        s++;
+      }
+      return s;
+    }
+    template<class T>
+    typename enable_if<typename T::MapIt::Value::LpRow, int>::type
+    addRowSet(T &t, dummy<2> = 2) {
+      int s=0;
+      for(typename T::MapIt i(t); i!=INVALID; ++i)
+        {
+          i.set(addRow());
+          s++;
+        }
+      return s;
+    }
+#endif
+
+    ///Set a row (i.e a constraint) of the LP
+
+    ///\param r is the row to be modified
+    ///\param l is lower bound (-\ref INF means no bound)
+    ///\param e is a linear expression (see \ref Expr)
+    ///\param u is the upper bound (\ref INF means no bound)
+    void row(Row r, Value l, const Expr &e, Value u) {
+      e.simplify();
+      _setRowCoeffs(rows(id(r)), ExprIterator(e.comps.begin(), cols),
+                    ExprIterator(e.comps.end(), cols));
+      _setRowLowerBound(rows(id(r)),l - *e);
+      _setRowUpperBound(rows(id(r)),u - *e);
+    }
+
+    ///Set a row (i.e a constraint) of the LP
+
+    ///\param r is the row to be modified
+    ///\param c is a linear expression (see \ref Constr)
+    void row(Row r, const Constr &c) {
+      row(r, c.lowerBounded()?c.lowerBound():-INF,
+          c.expr(), c.upperBounded()?c.upperBound():INF);
+    }
+
+
+    ///Get a row (i.e a constraint) of the LP
+
+    ///\param r is the row to get
+    ///\return the expression associated to the row
+    Expr row(Row r) const {
+      Expr e;
+      _getRowCoeffs(rows(id(r)), InsertIterator(e.comps, cols));
+      return e;
+    }
+
+    ///Add a new row (i.e a new constraint) to the LP
+
+    ///\param l is the lower bound (-\ref INF means no bound)
+    ///\param e is a linear expression (see \ref Expr)
+    ///\param u is the upper bound (\ref INF means no bound)
+    ///\return The created row.
+    Row addRow(Value l,const Expr &e, Value u) {
+      Row r;
+      e.simplify();
+      r._id = _addRowId(_addRow(l - *e, ExprIterator(e.comps.begin(), cols),
+                                ExprIterator(e.comps.end(), cols), u - *e));
+      return r;
+    }
+
+    ///Add a new row (i.e a new constraint) to the LP
+
+    ///\param c is a linear expression (see \ref Constr)
+    ///\return The created row.
+    Row addRow(const Constr &c) {
+      Row r;
+      c.expr().simplify();
+      r._id = _addRowId(_addRow(c.lowerBounded()?c.lowerBound():-INF, 
+                                ExprIterator(c.expr().comps.begin(), cols),
+                                ExprIterator(c.expr().comps.end(), cols),
+                                c.upperBounded()?c.upperBound():INF));
+      return r;
+    }
+    ///Erase a column (i.e a variable) from the LP
+
+    ///\param c is the column to be deleted
+    void erase(Col c) {
+      _eraseCol(cols(id(c)));
+      _eraseColId(cols(id(c)));
+    }
+    ///Erase a row (i.e a constraint) from the LP
+
+    ///\param r is the row to be deleted
+    void erase(Row r) {
+      _eraseRow(rows(id(r)));
+      _eraseRowId(rows(id(r)));
+    }
+
+    /// Get the name of a column
+
+    ///\param c is the coresponding column
+    ///\return The name of the colunm
+    std::string colName(Col c) const {
+      std::string name;
+      _getColName(cols(id(c)), name);
+      return name;
+    }
+
+    /// Set the name of a column
+
+    ///\param c is the coresponding column
+    ///\param name The name to be given
+    void colName(Col c, const std::string& name) {
+      _setColName(cols(id(c)), name);
+    }
+
+    /// Get the column by its name
+
+    ///\param name The name of the column
+    ///\return the proper column or \c INVALID
+    Col colByName(const std::string& name) const {
+      int k = _colByName(name);
+      return k != -1 ? Col(cols[k]) : Col(INVALID);
+    }
+
+    /// Get the name of a row
+
+    ///\param r is the coresponding row
+    ///\return The name of the row
+    std::string rowName(Row r) const {
+      std::string name;
+      _getRowName(rows(id(r)), name);
+      return name;
+    }
+
+    /// Set the name of a row
+
+    ///\param r is the coresponding row
+    ///\param name The name to be given
+    void rowName(Row r, const std::string& name) {
+      _setRowName(rows(id(r)), name);
+    }
+
+    /// Get the row by its name
+
+    ///\param name The name of the row
+    ///\return the proper row or \c INVALID
+    Row rowByName(const std::string& name) const {
+      int k = _rowByName(name);
+      return k != -1 ? Row(rows[k]) : Row(INVALID);
+    }
+
+    /// Set an element of the coefficient matrix of the LP
+
+    ///\param r is the row of the element to be modified
+    ///\param c is the column of the element to be modified
+    ///\param val is the new value of the coefficient
+    void coeff(Row r, Col c, Value val) {
+      _setCoeff(rows(id(r)),cols(id(c)), val);
+    }
+
+    /// Get an element of the coefficient matrix of the LP
+
+    ///\param r is the row of the element
+    ///\param c is the column of the element
+    ///\return the corresponding coefficient
+    Value coeff(Row r, Col c) const {
+      return _getCoeff(rows(id(r)),cols(id(c)));
+    }
+
+    /// Set the lower bound of a column (i.e a variable)
+
+    /// The lower bound of a variable (column) has to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value or -\ref INF.
+    void colLowerBound(Col c, Value value) {
+      _setColLowerBound(cols(id(c)),value);
+    }
+
+    /// Get the lower bound of a column (i.e a variable)
+
+    /// This function returns the lower bound for column (variable) \c c
+    /// (this might be -\ref INF as well).
+    ///\return The lower bound for column \c c
+    Value colLowerBound(Col c) const {
+      return _getColLowerBound(cols(id(c)));
+    }
+
+    ///\brief Set the lower bound of  several columns
+    ///(i.e variables) at once
+    ///
+    ///This magic function takes a container as its argument
+    ///and applies the function on all of its elements.
+    ///The lower bound of a variable (column) has to be given by an
+    ///extended number of type Value, i.e. a finite number of type
+    ///Value or -\ref INF.
+#ifdef DOXYGEN
+    template<class T>
+    void colLowerBound(T &t, Value value) { return 0;}
+#else
+    template<class T>
+    typename enable_if<typename T::value_type::LpCol,void>::type
+    colLowerBound(T &t, Value value,dummy<0> = 0) {
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        colLowerBound(*i, value);
+      }
+    }
+    template<class T>
+    typename enable_if<typename T::value_type::second_type::LpCol,
+                       void>::type
+    colLowerBound(T &t, Value value,dummy<1> = 1) {
+      for(typename T::iterator i=t.begin();i!=t.end();++i) {
+        colLowerBound(i->second, value);
+      }
+    }
+    template<class T>
+    typename enable_if<typename T::MapIt::Value::LpCol,
+                       void>::type
+    colLowerBound(T &t, Value value,dummy<2> = 2) {
+      for(typename T::MapIt i(t); i!=INVALID; ++i){
+        colLowerBound(*i, value);
+      }
+    }
+#endif
+
+    /// Set the upper bound of a column (i.e a variable)
+
+    /// The upper bound of a variable (column) has to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value or \ref INF.
+    void colUpperBound(Col c, Value value) {
+      _setColUpperBound(cols(id(c)),value);
+    };
+
+    /// Get the upper bound of a column (i.e a variable)
+
+    /// This function returns the upper bound for column (variable) \c c
+    /// (this might be \ref INF as well).
+    /// \return The upper bound for column \c c
+    Value colUpperBound(Col c) const {
+      return _getColUpperBound(cols(id(c)));
+    }
+
+    ///\brief Set the upper bound of  several columns
+    ///(i.e variables) at once
+    ///
+    ///This magic function takes a container as its argument
+    ///and applies the function on all of its elements.
+    ///The upper bound of a variable (column) has to be given by an
+    ///extended number of type Value, i.e. a finite number of type
+    ///Value or \ref INF.
+#ifdef DOXYGEN
+    template<class T>
+    void colUpperBound(T &t, Value value) { return 0;}
+#else
+    template<class T1>
+    typename enable_if<typename T1::value_type::LpCol,void>::type
+    colUpperBound(T1 &t, Value value,dummy<0> = 0) {
+      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
+        colUpperBound(*i, value);
+      }
+    }
+    template<class T1>
+    typename enable_if<typename T1::value_type::second_type::LpCol,
+                       void>::type
+    colUpperBound(T1 &t, Value value,dummy<1> = 1) {
+      for(typename T1::iterator i=t.begin();i!=t.end();++i) {
+        colUpperBound(i->second, value);
+      }
+    }
+    template<class T1>
+    typename enable_if<typename T1::MapIt::Value::LpCol,
+                       void>::type
+    colUpperBound(T1 &t, Value value,dummy<2> = 2) {
+      for(typename T1::MapIt i(t); i!=INVALID; ++i){
+        colUpperBound(*i, value);
+      }
+    }
+#endif
+
+    /// Set the lower and the upper bounds of a column (i.e a variable)
+
+    /// The lower and the upper bounds of
+    /// a variable (column) have to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value, -\ref INF or \ref INF.
+    void colBounds(Col c, Value lower, Value upper) {
+      _setColLowerBound(cols(id(c)),lower);
+      _setColUpperBound(cols(id(c)),upper);
+    }
+
+    ///\brief Set the lower and the upper bound of several columns
+    ///(i.e variables) at once
+    ///
+    ///This magic function takes a container as its argument
+    ///and applies the function on all of its elements.
+    /// The lower and the upper bounds of
+    /// a variable (column) have to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value, -\ref INF or \ref INF.
+#ifdef DOXYGEN
+    template<class T>
+    void colBounds(T &t, Value lower, Value upper) { return 0;}
+#else
+    template<class T2>
+    typename enable_if<typename T2::value_type::LpCol,void>::type
+    colBounds(T2 &t, Value lower, Value upper,dummy<0> = 0) {
+      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
+        colBounds(*i, lower, upper);
+      }
+    }
+    template<class T2>
+    typename enable_if<typename T2::value_type::second_type::LpCol, void>::type
+    colBounds(T2 &t, Value lower, Value upper,dummy<1> = 1) {
+      for(typename T2::iterator i=t.begin();i!=t.end();++i) {
+        colBounds(i->second, lower, upper);
+      }
+    }
+    template<class T2>
+    typename enable_if<typename T2::MapIt::Value::LpCol, void>::type
+    colBounds(T2 &t, Value lower, Value upper,dummy<2> = 2) {
+      for(typename T2::MapIt i(t); i!=INVALID; ++i){
+        colBounds(*i, lower, upper);
+      }
+    }
+#endif
+
+    /// Set the lower bound of a row (i.e a constraint)
+
+    /// The lower bound of a constraint (row) has to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value or -\ref INF.
+    void rowLowerBound(Row r, Value value) {
+      _setRowLowerBound(rows(id(r)),value);
+    }
+
+    /// Get the lower bound of a row (i.e a constraint)
+
+    /// This function returns the lower bound for row (constraint) \c c
+    /// (this might be -\ref INF as well).
+    ///\return The lower bound for row \c r
+    Value rowLowerBound(Row r) const {
+      return _getRowLowerBound(rows(id(r)));
+    }
+
+    /// Set the upper bound of a row (i.e a constraint)
+
+    /// The upper bound of a constraint (row) has to be given by an
+    /// extended number of type Value, i.e. a finite number of type
+    /// Value or -\ref INF.
+    void rowUpperBound(Row r, Value value) {
+      _setRowUpperBound(rows(id(r)),value);
+    }
+
+    /// Get the upper bound of a row (i.e a constraint)
+
+    /// This function returns the upper bound for row (constraint) \c c
+    /// (this might be -\ref INF as well).
+    ///\return The upper bound for row \c r
+    Value rowUpperBound(Row r) const {
+      return _getRowUpperBound(rows(id(r)));
+    }
+
+    ///Set an element of the objective function
+    void objCoeff(Col c, Value v) {_setObjCoeff(cols(id(c)),v); };
+
+    ///Get an element of the objective function
+    Value objCoeff(Col c) const { return _getObjCoeff(cols(id(c))); };
+
+    ///Set the objective function
+
+    ///\param e is a linear expression of type \ref Expr.
+    ///
+    void obj(const Expr& e) {
+      _setObjCoeffs(ExprIterator(e.comps.begin(), cols),
+                    ExprIterator(e.comps.end(), cols));
+      obj_const_comp = *e;
+    }
+
+    ///Get the objective function
+
+    ///\return the objective function as a linear expression of type
+    ///Expr.
+    Expr obj() const {
+      Expr e;
+      _getObjCoeffs(InsertIterator(e.comps, cols));
+      *e = obj_const_comp;
+      return e;
+    }
+
+
+    ///Set the direction of optimization
+    void sense(Sense sense) { _setSense(sense); }
+
+    ///Query the direction of the optimization
+    Sense sense() const {return _getSense(); }
+
+    ///Set the sense to maximization
+    void max() { _setSense(MAX); }
+
+    ///Set the sense to maximization
+    void min() { _setSense(MIN); }
+
+    ///Clears the problem
+    void clear() { _clear(); }
+
+    /// Sets the message level of the solver
+    void messageLevel(MessageLevel level) { _messageLevel(level); }
+
+    ///@}
+
+  };
+
+  /// Addition
+
+  ///\relates LpBase::Expr
+  ///
+  inline LpBase::Expr operator+(const LpBase::Expr &a, const LpBase::Expr &b) {
+    LpBase::Expr tmp(a);
+    tmp+=b;
+    return tmp;
+  }
+  ///Substraction
+
+  ///\relates LpBase::Expr
+  ///
+  inline LpBase::Expr operator-(const LpBase::Expr &a, const LpBase::Expr &b) {
+    LpBase::Expr tmp(a);
+    tmp-=b;
+    return tmp;
+  }
+  ///Multiply with constant
+
+  ///\relates LpBase::Expr
+  ///
+  inline LpBase::Expr operator*(const LpBase::Expr &a, const LpBase::Value &b) {
+    LpBase::Expr tmp(a);
+    tmp*=b;
+    return tmp;
+  }
+
+  ///Multiply with constant
+
+  ///\relates LpBase::Expr
+  ///
+  inline LpBase::Expr operator*(const LpBase::Value &a, const LpBase::Expr &b) {
+    LpBase::Expr tmp(b);
+    tmp*=a;
+    return tmp;
+  }
+  ///Divide with constant
+
+  ///\relates LpBase::Expr
+  ///
+  inline LpBase::Expr operator/(const LpBase::Expr &a, const LpBase::Value &b) {
+    LpBase::Expr tmp(a);
+    tmp/=b;
+    return tmp;
+  }
+
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator<=(const LpBase::Expr &e,
+                                   const LpBase::Expr &f) {
+    return LpBase::Constr(0, f - e, LpBase::INF);
+  }
+
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator<=(const LpBase::Value &e,
+                                   const LpBase::Expr &f) {
+    return LpBase::Constr(e, f, LpBase::NaN);
+  }
+
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator<=(const LpBase::Expr &e,
+                                   const LpBase::Value &f) {
+    return LpBase::Constr(- LpBase::INF, e, f);
+  }
+
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator>=(const LpBase::Expr &e,
+                                   const LpBase::Expr &f) {
+    return LpBase::Constr(0, e - f, LpBase::INF);
+  }
+
+
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator>=(const LpBase::Value &e,
+                                   const LpBase::Expr &f) {
+    return LpBase::Constr(LpBase::NaN, f, e);
+  }
+
+
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator>=(const LpBase::Expr &e,
+                                   const LpBase::Value &f) {
+    return LpBase::Constr(f, e, LpBase::INF);
+  }
+
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator==(const LpBase::Expr &e,
+                                   const LpBase::Value &f) {
+    return LpBase::Constr(f, e, f);
+  }
+
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator==(const LpBase::Expr &e,
+                                   const LpBase::Expr &f) {
+    return LpBase::Constr(0, f - e, 0);
+  }
+
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator<=(const LpBase::Value &n,
+                                   const LpBase::Constr &c) {
+    LpBase::Constr tmp(c);
+    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
+    tmp.lowerBound()=n;
+    return tmp;
+  }
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator<=(const LpBase::Constr &c,
+                                   const LpBase::Value &n)
+  {
+    LpBase::Constr tmp(c);
+    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
+    tmp.upperBound()=n;
+    return tmp;
+  }
+
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator>=(const LpBase::Value &n,
+                                   const LpBase::Constr &c) {
+    LpBase::Constr tmp(c);
+    LEMON_ASSERT(isNaN(tmp.upperBound()), "Wrong LP constraint");
+    tmp.upperBound()=n;
+    return tmp;
+  }
+  ///Create constraint
+
+  ///\relates LpBase::Constr
+  ///
+  inline LpBase::Constr operator>=(const LpBase::Constr &c,
+                                   const LpBase::Value &n)
+  {
+    LpBase::Constr tmp(c);
+    LEMON_ASSERT(isNaN(tmp.lowerBound()), "Wrong LP constraint");
+    tmp.lowerBound()=n;
+    return tmp;
+  }
+
+  ///Addition
+
+  ///\relates LpBase::DualExpr
+  ///
+  inline LpBase::DualExpr operator+(const LpBase::DualExpr &a,
+                                    const LpBase::DualExpr &b) {
+    LpBase::DualExpr tmp(a);
+    tmp+=b;
+    return tmp;
+  }
+  ///Substraction
+
+  ///\relates LpBase::DualExpr
+  ///
+  inline LpBase::DualExpr operator-(const LpBase::DualExpr &a,
+                                    const LpBase::DualExpr &b) {
+    LpBase::DualExpr tmp(a);
+    tmp-=b;
+    return tmp;
+  }
+  ///Multiply with constant
+
+  ///\relates LpBase::DualExpr
+  ///
+  inline LpBase::DualExpr operator*(const LpBase::DualExpr &a,
+                                    const LpBase::Value &b) {
+    LpBase::DualExpr tmp(a);
+    tmp*=b;
+    return tmp;
+  }
+
+  ///Multiply with constant
+
+  ///\relates LpBase::DualExpr
+  ///
+  inline LpBase::DualExpr operator*(const LpBase::Value &a,
+                                    const LpBase::DualExpr &b) {
+    LpBase::DualExpr tmp(b);
+    tmp*=a;
+    return tmp;
+  }
+  ///Divide with constant
+
+  ///\relates LpBase::DualExpr
+  ///
+  inline LpBase::DualExpr operator/(const LpBase::DualExpr &a,
+                                    const LpBase::Value &b) {
+    LpBase::DualExpr tmp(a);
+    tmp/=b;
+    return tmp;
+  }
+
+  /// \ingroup lp_group
+  ///
+  /// \brief Common base class for LP solvers
+  ///
+  /// This class is an abstract base class for LP solvers. This class
+  /// provides a full interface for set and modify an LP problem,
+  /// solve it and retrieve the solution. You can use one of the
+  /// descendants as a concrete implementation, or the \c Lp
+  /// default LP solver. However, if you would like to handle LP
+  /// solvers as reference or pointer in a generic way, you can use
+  /// this class directly.
+  class LpSolver : virtual public LpBase {
+  public:
+
+    /// The problem types for primal and dual problems
+    enum ProblemType {
+      /// = 0. Feasible solution hasn't been found (but may exist).
+      UNDEFINED = 0,
+      /// = 1. The problem has no feasible solution.
+      INFEASIBLE = 1,
+      /// = 2. Feasible solution found.
+      FEASIBLE = 2,
+      /// = 3. Optimal solution exists and found.
+      OPTIMAL = 3,
+      /// = 4. The cost function is unbounded.
+      UNBOUNDED = 4
+    };
+
+    ///The basis status of variables
+    enum VarStatus {
+      /// The variable is in the basis
+      BASIC, 
+      /// The variable is free, but not basic
+      FREE,
+      /// The variable has active lower bound 
+      LOWER,
+      /// The variable has active upper bound
+      UPPER,
+      /// The variable is non-basic and fixed
+      FIXED
+    };
+
+  protected:
+
+    virtual SolveExitStatus _solve() = 0;
+
+    virtual Value _getPrimal(int i) const = 0;
+    virtual Value _getDual(int i) const = 0;
+
+    virtual Value _getPrimalRay(int i) const = 0;
+    virtual Value _getDualRay(int i) const = 0;
+
+    virtual Value _getPrimalValue() const = 0;
+
+    virtual VarStatus _getColStatus(int i) const = 0;
+    virtual VarStatus _getRowStatus(int i) const = 0;
+
+    virtual ProblemType _getPrimalType() const = 0;
+    virtual ProblemType _getDualType() const = 0;
+
+  public:
+
+    ///Allocate a new LP problem instance
+    virtual LpSolver* newSolver() const = 0;
+    ///Make a copy of the LP problem
+    virtual LpSolver* cloneSolver() const = 0;
+
+    ///\name Solve the LP
+
+    ///@{
+
+    ///\e Solve the LP problem at hand
+    ///
+    ///\return The result of the optimization procedure. Possible
+    ///values and their meanings can be found in the documentation of
+    ///\ref SolveExitStatus.
+    SolveExitStatus solve() { return _solve(); }
+
+    ///@}
+
+    ///\name Obtain the Solution
+
+    ///@{
+
+    /// The type of the primal problem
+    ProblemType primalType() const {
+      return _getPrimalType();
+    }
+
+    /// The type of the dual problem
+    ProblemType dualType() const {
+      return _getDualType();
+    }
+
+    /// Return the primal value of the column
+
+    /// Return the primal value of the column.
+    /// \pre The problem is solved.
+    Value primal(Col c) const { return _getPrimal(cols(id(c))); }
+
+    /// Return the primal value of the expression
+
+    /// Return the primal value of the expression, i.e. the dot
+    /// product of the primal solution and the expression.
+    /// \pre The problem is solved.
+    Value primal(const Expr& e) const {
+      double res = *e;
+      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
+        res += *c * primal(c);
+      }
+      return res;
+    }
+    /// Returns a component of the primal ray
+    
+    /// The primal ray is solution of the modified primal problem,
+    /// where we change each finite bound to 0, and we looking for a
+    /// negative objective value in case of minimization, and positive
+    /// objective value for maximization. If there is such solution,
+    /// that proofs the unsolvability of the dual problem, and if a
+    /// feasible primal solution exists, then the unboundness of
+    /// primal problem.
+    ///
+    /// \pre The problem is solved and the dual problem is infeasible.
+    /// \note Some solvers does not provide primal ray calculation
+    /// functions.
+    Value primalRay(Col c) const { return _getPrimalRay(cols(id(c))); }
+
+    /// Return the dual value of the row
+
+    /// Return the dual value of the row.
+    /// \pre The problem is solved.
+    Value dual(Row r) const { return _getDual(rows(id(r))); }
+
+    /// Return the dual value of the dual expression
+
+    /// Return the dual value of the dual expression, i.e. the dot
+    /// product of the dual solution and the dual expression.
+    /// \pre The problem is solved.
+    Value dual(const DualExpr& e) const {
+      double res = 0.0;
+      for (DualExpr::ConstCoeffIt r(e); r != INVALID; ++r) {
+        res += *r * dual(r);
+      }
+      return res;
+    }
+
+    /// Returns a component of the dual ray
+    
+    /// The dual ray is solution of the modified primal problem, where
+    /// we change each finite bound to 0 (i.e. the objective function
+    /// coefficients in the primal problem), and we looking for a
+    /// ositive objective value. If there is such solution, that
+    /// proofs the unsolvability of the primal problem, and if a
+    /// feasible dual solution exists, then the unboundness of
+    /// dual problem.
+    ///
+    /// \pre The problem is solved and the primal problem is infeasible.
+    /// \note Some solvers does not provide dual ray calculation
+    /// functions.
+    Value dualRay(Row r) const { return _getDualRay(rows(id(r))); }
+
+    /// Return the basis status of the column
+
+    /// \see VarStatus
+    VarStatus colStatus(Col c) const { return _getColStatus(cols(id(c))); }
+
+    /// Return the basis status of the row
+
+    /// \see VarStatus
+    VarStatus rowStatus(Row r) const { return _getRowStatus(rows(id(r))); }
+
+    ///The value of the objective function
+
+    ///\return
+    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
+    /// of the primal problem, depending on whether we minimize or maximize.
+    ///- \ref NaN if no primal solution is found.
+    ///- The (finite) objective value if an optimal solution is found.
+    Value primal() const { return _getPrimalValue()+obj_const_comp;}
+    ///@}
+
+  protected:
+
+  };
+
+
+  /// \ingroup lp_group
+  ///
+  /// \brief Common base class for MIP solvers
+  ///
+  /// This class is an abstract base class for MIP solvers. This class
+  /// provides a full interface for set and modify an MIP problem,
+  /// solve it and retrieve the solution. You can use one of the
+  /// descendants as a concrete implementation, or the \c Lp
+  /// default MIP solver. However, if you would like to handle MIP
+  /// solvers as reference or pointer in a generic way, you can use
+  /// this class directly.
+  class MipSolver : virtual public LpBase {
+  public:
+
+    /// The problem types for MIP problems
+    enum ProblemType {
+      /// = 0. Feasible solution hasn't been found (but may exist).
+      UNDEFINED = 0,
+      /// = 1. The problem has no feasible solution.
+      INFEASIBLE = 1,
+      /// = 2. Feasible solution found.
+      FEASIBLE = 2,
+      /// = 3. Optimal solution exists and found.
+      OPTIMAL = 3,
+      /// = 4. The cost function is unbounded.
+      ///The Mip or at least the relaxed problem is unbounded.
+      UNBOUNDED = 4
+    };
+
+    ///Allocate a new MIP problem instance
+    virtual MipSolver* newSolver() const = 0;
+    ///Make a copy of the MIP problem
+    virtual MipSolver* cloneSolver() const = 0;
+
+    ///\name Solve the MIP
+
+    ///@{
+
+    /// Solve the MIP problem at hand
+    ///
+    ///\return The result of the optimization procedure. Possible
+    ///values and their meanings can be found in the documentation of
+    ///\ref SolveExitStatus.
+    SolveExitStatus solve() { return _solve(); }
+
+    ///@}
+
+    ///\name Set Column Type
+    ///@{
+
+    ///Possible variable (column) types (e.g. real, integer, binary etc.)
+    enum ColTypes {
+      /// = 0. Continuous variable (default).
+      REAL = 0,
+      /// = 1. Integer variable.
+      INTEGER = 1
+    };
+
+    ///Sets the type of the given column to the given type
+
+    ///Sets the type of the given column to the given type.
+    ///
+    void colType(Col c, ColTypes col_type) {
+      _setColType(cols(id(c)),col_type);
+    }
+
+    ///Gives back the type of the column.
+
+    ///Gives back the type of the column.
+    ///
+    ColTypes colType(Col c) const {
+      return _getColType(cols(id(c)));
+    }
+    ///@}
+
+    ///\name Obtain the Solution
+
+    ///@{
+
+    /// The type of the MIP problem
+    ProblemType type() const {
+      return _getType();
+    }
+
+    /// Return the value of the row in the solution
+
+    ///  Return the value of the row in the solution.
+    /// \pre The problem is solved.
+    Value sol(Col c) const { return _getSol(cols(id(c))); }
+
+    /// Return the value of the expression in the solution
+
+    /// Return the value of the expression in the solution, i.e. the
+    /// dot product of the solution and the expression.
+    /// \pre The problem is solved.
+    Value sol(const Expr& e) const {
+      double res = *e;
+      for (Expr::ConstCoeffIt c(e); c != INVALID; ++c) {
+        res += *c * sol(c);
+      }
+      return res;
+    }
+    ///The value of the objective function
+    
+    ///\return
+    ///- \ref INF or -\ref INF means either infeasibility or unboundedness
+    /// of the problem, depending on whether we minimize or maximize.
+    ///- \ref NaN if no primal solution is found.
+    ///- The (finite) objective value if an optimal solution is found.
+    Value solValue() const { return _getSolValue()+obj_const_comp;}
+    ///@}
+
+  protected:
+
+    virtual SolveExitStatus _solve() = 0;
+    virtual ColTypes _getColType(int col) const = 0;
+    virtual void _setColType(int col, ColTypes col_type) = 0;
+    virtual ProblemType _getType() const = 0;
+    virtual Value _getSol(int i) const = 0;
+    virtual Value _getSolValue() const = 0;
+
+  };
+
+
+
+} //namespace lemon
+
+#endif //LEMON_LP_BASE_H